428 
R. A. FISHER ON THE CORRELATION BETWEEN 
25. The Interpretation of the Statistical Effects of Dominance. — The results 
which we have obtained, although subject to large probable errors and to theoretical 
reservations which render an exact estimate of these errors impossible, suggest that 
the ratio % , the statistical measure of the extent of dominance, has values of about 
’25 to '38. In his initial memoir on this subject Karl Pearson has shown that, 
under the restricted conditions there considered, this ratio should be exactly 
Subsequently Udny Ytjle (Conference on Genetics) pointed out that the parental 
correlation could be raised from the low values reached in that memoir to values 
more in accordance with the available figures by the partial or total abandonment of 
the assumption of dominance. To this view Professor Pearson subsequently gave 
his approval ; but it does not seem to have been observed that if lower values are 
required — and our analysis tends to show that they are not— the statistical effects are 
governed not only by the physical ratio — , but by the proportions in which the three 
Mendelian phases are present. This effect is an important one, and very considerably 
modifies the conclusions which we should draw from any observed value of the 
dominance ratio. 
The fraction - 5 - , of which the numerator and denominator are the contributions of 
a i 
a single factor to e 2 and v 2 , is equal, as we have seen (Article 5, equations V-VII) to 
' 2 pqd 2 
(p + q) 2 a l - 2 (p 2 - <f)cid + (p 2 + q 2 )d 2 ’ 
and depends wholly upon the two ratios - and . We may therefore represent the 
variations of this function by drawing the curves for which it has a series of constant 
values upon a plane, each point on which is specified by a pair of particular values 
for these two ratios. The accompanying diagram (fig. 1 , p. 430) shows such a series of 
curves, using — and log as co-ordinates. The logarithm is chosen as a variable, 
because equal intensity of selection will affect this quantity to an equal extent, what- 
ever may be its value ; it also possesses the great advantage of showing reciprocal 
values of - in symmetrical positions. 
It will be seen that 3 is not by any means the highest value possible : when d = a, 
and when ^ is very great, any value up to unity may appear ; but high values are 
confined to this restricted region. When — is less than '3 the ratio is never greater 
than '05, and we cannot get values as high as '15 unless - be as great as '5, On the 
